How to draw normal map?
It is easier and more intuitive to paint a height-map, then convert it into a normal map:



There is GIMP normalmap plugin, Photoshop plugins like xNormal, apps like CrazyBump and a lot of others. These all can do the conversion. Also, it can be done through Blender Baking.

If you already have a normal map, and you need to add to it, you can combine normal maps with overlay blending operation - generally it is ok enough but note that it is not the correct operation - more on combining normal maps is here: Blending in detail. 

You can also paint directly into normal maps:


you can erase with RGB[128,128,255] brush
you can average with ordinary Soften (smooth) brush
you can smudge with Smear brush
you can paint with a special texture brush:


create a brush height texture that you want to paint with
convert to normal map texture


paint with this texture in overlay mode. It will be like sculpting, but on a texture. The brush color must be white, spacing of strokes very low and strength of brush also low